ELLIPTIC FLOW FROM THERMAL AND KLN INITIAL CONDITIONS

Dr. Marco Ruggieri Dipartimento di Fisica e Astronomia, Università degli Studi di Catania, Catania (Italy) ELLIPTIC FLOW FROM THERMAL AND KLN INITIAL CONDITIONS Based on collaboration with: V. Greco, S. Plumari and F. Scardina Kyoto, 2013 December 10

In this talk: Very short introduction to heavy ion collisions Transport theory and heavy ion collisions Thermalization Elliptic flow computation Conclusions and Outlook

A QGP in Heavy Ion Collisions B Impact parameter direction Collision direction Impact parameter direction Collision (flight) direction A,B: Cu, Au (RHIC@BNL) Pb (LHC@CERN). FIREBALL: Hot and dense expanding parton mixture: QUARK-GLUON-PLASMA (QGP) T about 10 12 K, t about 10-23 seconds

M. R. et al., in preparation QGP in Heavy Ion Collisions Inner core temperature (simulation) QCD-Tc Initial temperature much larger than QCD critical temperature: Description in terms of partons is appropriate.

Elliptic flow Particle multiplicity in momentum space J. Y. Ollitraut, PRD46 (1992) Elliptic flow: leading contribution to anisotropy in momentum space y f p T x Immediately after the collision, pressure gradient along X is larger than that along Y. As a consequence, the medium expands preferentially along the short axis of the ellipse, creating a flow. Collision direction Impact parameter direction

Elliptic flow J. Y. Ollitraut, PRD46 (1992) Expansion Interactions Transfer of anisotropy M. R. et al., in preparation

Boltzmann equation and QGP In order to simulate the temporal evolution of the fireball we solve the Boltzmann equation for the parton distribution function f: L. Boltzmann, 1872 Drift term For the case of 12->1 2 processes: Collision integral Drift term: change of f due to particles flowing into and out of the phase space volume centered at (x,p). Collision integral: change of f due to collision processes in the phase space volume centered at (x,p). p 1 w p 1 p 2 p 2

eta/s: hydro by transport We use Boltzmann equation to simulate a fluid at fixed eta/s. Total Cross section is computed in each configuration space cell according to Chapman- Enskog equation to give the wished value of eta/s. Plumari et al., Phys. Rev. C86 (2012). Greco et al., Phys. Lett. B670 (2009). Plumari et al., J.Phys.Conf.Ser. 420 (2013).

eta/s: hydro by transport We use Boltzmann equation to simulate a fluid at fixed eta/s. Total Cross section is computed in each configuration space cell according to Chapman- Enskog equation to give the wished value of eta/s. (.) Collision integral is gauged in each cell to assure that the fluid dissipates according to the desired value of eta/s. (.) Microscopic details are not important: the specific microscopic process producing eta/s is not relevant, only macroscopic quantities are, in analogy with hydrodynamics. Plumari et al., Phys. Rev. C86 (2012). Greco et al., Phys. Lett. B670 (2009). Plumari et al., J.Phys.Conf.Ser. 420 (2013).

eta/s: hydro by transport We use Boltzmann equation to simulate a fluid at fixed eta/s. Total Cross section is computed in each configuration space cell according to Chapman- Enskog equation to give the wished value of eta/s. (.) Collision integral is gauged in each cell to assure that the fluid dissipates according to the desired value of eta/s. (.) Microscopic details are not important: the specific microscopic process producing eta/s is not relevant, only macroscopic quantities are, in analogy with hydrodynamics. Transport Description in terms of parton distribution function bridge Hydro Dynamical evolution governed by macroscopic quantities

eta/s: hydro by transport We use Boltzmann equation to simulate a fluid at fixed eta/s. Total Cross section is computed in each configuration space cell according to Chapman- Enskog equation to give the wished value of eta/s. (.) Collision integral is gauged in each cell to assure that the fluid dissipates according to the desired value of eta/s. (.) Microscopic details are not important: the specific microscopic process producing eta/s is not relevant, only macroscopic quantities are, in analogy with hydrodynamics. Transport bridge Hydro Non perturbative description: we never assume coupling is small.

eta/s: hydro by transport We use Boltzmann equation to simulate a fluid at fixed eta/s. Total Cross section is computed in each configuration space cell according to Chapman- Enskog equation to give the wished value of eta/s. Huovinen and Molnar, PRC79 (2009) There is agreement of hydro with transport also in the non dilute limit

eta/s: hydro by transport We use Boltzmann equation to simulate a fluid at fixed eta/s. Total Cross section is computed in each configuration space cell according to Chapman- Enskog equation to give the wished value of eta/s. Transport Hydro Bhalerao et al., PLB627 (2005) There is agreement of hydro with transport also in the non dilute limit

eta/s: hydro by transport We use Boltzmann equation to simulate a fluid at fixed eta/s. Total Cross section is computed in each configuration space cell according to Chapman- Enskog equation to give the wished value of eta/s. Kinetic freezout A smooth kinetic freezout is implemented in order to gradually reduce the strength of the interactions as the temperature decreases below the critical temperature.

eta/s: hydro by transport Temperature dependence of eta/s already appeared in the literature recently. H. Niemi et al., PRC86 (2012), PRL106 (2011) Shen and Heinz, PRC83 (2011)

Initial condition: Glasma CGC McLerran and Venugopalan, PRD 49, 2233 (1994) McLerran and Venugopalan, PRD 49, 3352 (1994) Glasma collision Reviews/Lectures McLerran, 2011 Iancu, 2009 McLerran, 2009 Lappi, 2010 Gelis, 2010 Fukushima, 2011 Lappi and McLerran, Nucl. Phys. A772 (2006) Decay of flux tubes to parton liquid should occur on a timescale 1/Qs

For Pb-Pb collision average Qs can be larger [Lappi, EPJC71 (2011)] Initial condition: fkln Nardi et al., Nucl. Phys. A747, 609 (2005) (f)kln spectrum Kharzeev et al., Phys. Lett. B561, 93 (2003) Nardi et al., Phys. Lett. B507, 121 (2001) Drescher and Nara, PRC75, 034905 (2007) Hirano and Nara, PRC79, 064904 (2009) Hirano and Nara, Nucl. Phys. A743, 305 (2004) Albacete and Dumitru, arxiv:1011.5161[hep-ph] Saturation effects built in the ugdfs.

Few remarks on KLN fkln is not glasma [Blaizot et al., NPA846 (2010)] It is not our purpose to insist on exact reproduction of experimental data [Gale et al., PRL110 (2013)] Rather we want to check the role of the initial distribution in momentum space Hydro widely uses KLN, and we are interested to compare the two approaches Viscometer: Schen et al., arxiv1308:2111 Thermometer: Schen et al., arxiv1308:2440 Flow computations: Ollitrault et al., arxiv1311:5339 Drescher and Nara, PRC75 (2007) Hirano and Nara, PRC79 (2009) Hirano and Nara, NPA743 (2004)

Initial condition: Th-Glauber (Almost) Geometrical description of the fireball: Assuming a nucleon distribution in the parents nuclei (typically a Woods-Saxon), one counts how many particles from each nucleus are present in the overlap region; among them, the participants are the nucleons that effectively can have an interaction (in fact, the particles that are in the overlap region but do not interact, are not considered). For a review see: Miller et al., Ann.Rev.Nucl.Part.Sci. 57, 205 (2007)

Initial spectra M. R. et al., PLB727 (2013) M. R. et al., in preparation Our novelty: For fkln we consider the initial spectrum given by the theory at small transverse momenta.

Initial spectra M. R. et al., PLB727 (2013) M. R. et al., in preparation Assume different initial times Our novelty: For fkln we consider the initial spectrum given by the theory at small transverse momenta.

Thermalization M. R. et al., PLB727 (2013) M. R. et al., in preparation AuAu@200A GeV Final spectra of fkln and Th-Glauber coincide

Thermalization AuAu@200A GeV M. R. et al., PLB727 (2013) M. R. et al., in preparation Thermalization in less than 1 fm/c, in agreement with: Greiner et al., Nucl. Phys. A806, 287 (2008). Longitudinal direction Transverse plane Not so surprising: Because eta/s is small, large cross sections naturally lead to fast thermalization. However, interesting: We have dynamics in the early stages of the simulation, which prepares the momentum distribution to build up the elliptic flow.

M. R. et al., in preparation Thermalization Thermalization in less than 1 fm/c, in agreement with: Greiner et al., Nucl. Phys. A806, 287 (2008). Longitudinal direction Transverse plane Not so surprising: Because eta/s is small, large cross sections naturally lead to fast thermalization. However, interesting: We have dynamics in the early stages of the simulation, which prepares the momentum distribution to build up the elliptic flow.

M. R. et al., PLB727 (2013) M. R. et al., in preparation Elliptic flow from Transport Au-Au collision RHIC energy Hydro-like KLN initial. Larger eccentricity of KLN implies larger v 2 Results in fair agreement with hydro: Song et al., PRC83 (2011)

M. R. et al., PLB727 (2013) M. R. et al., in preparation Elliptic flow from Transport Au-Au collision RHIC energy Hydro-like KLN initial. Thermalized spectra Nonthermal spectra

M. R. et al., in preparation Elliptic flow from Transport Pb-Pb collision LHC energy Elliptic flow computations show this quantity is very sensitive to the initial conditions:.) Initial anisotropy (eccentricity).) Initial momentum distribution Measurements of elliptic flow in experiments might permit to identify the best theoretical initial conditions.

M. R. et al., in preparation Elliptic flow from Transport Au-Au collision RHIC energy Summary of the effect on differential v 2 b=7.5 fm b=9 fm b=5 fm b=2.5 fm For more central collisions the effect on v2 becomes milder.

Are micro-details important? small angle dominance fkln PbPb@2.76 TeV Same cross section used in: Zhang et al., PLB 455 (1999) Molnar and Gyulassy, NPA 697 (2002) Greco et al., PLB 670 (2009) Increasing m D makes the cross section isotropic. However: Strong change of the cross section does not result in a strong change of the elliptic flow. Q s2 =5 GeV 2 M. R. et al., in preparation

Invariant distributions M. R. et al., in preparation M. R. et al., work in progress Longitudinal and transverse expansions help to dilute the system, lowering the invariant distribution functions 1+f factors in the collision integral, arising from the bosonic nature of gluons, should not modify in a substantial way our results on elliptic flow Preliminary result: no change due to 1+f (at RHIC energy).

Conclusions QGP produced in heavy ion collisions behaves as a liquid rather than a gas, developing collective flows. Kinetic Theory permits to compute elliptic flow of plasma, as well as its thermalization times and isotropization efficiency. Initial distribution in momentum space affects the flow and the building up of momentum anisotropy.

Outlook (.)Bose-Einstein condensate BE condensation, in particular at LHC energy [Blaizot et al., NPA920 (2013), NPA873 (2012)] (.)Initial conditions from classical field dynamics Implementation of the proper initialization from glasma spectrum&eccentricity (.)Fluctuations in the initial condition Systematic study of higher order harmonics (.)Inelastic processes Implementation of 2 to 3 and 3 to 2 processes in the collision integral

Freedom creates doubts. (James Douglas Morrison)

Spectra and data M. R. et al., in preparation

Pressures: weak coupling M. R. et al., in preparation

Eccentricities M. R. et al., in preparation

Thermalization M. R. et al., PLB727 (2013) M. R. et al., in preparation AuAu@200A GeV Spectra AuAu@200A GeV Multiplicity

Fireball Isotropization M. R. et al., in preparation Complete isotropization in strong coupling (perfect gas would not be efficient to isotropize pressure)